Is this normal? Or is there a mental problem with me?

Most teenage girls feel fat or ugly. That part is normal, but you are most certainly either starting or are already going through some food problem (ex: anorexia/bulimia). But if you HAVE begun, you do not have it badly. You are still eating which is good. But you need to eat more. You are definitely skinny and fit :) So don't worry about that. I know, hearing it doesn't change anything. I know what you're going through, been there, done it. My advice is to seek help before this gets dangerous. I almost died when I was younger of malnutrition from not eating, and it is very scary. You don't wanna go down that road. Tell an adult you trust and they can get you help. It's scary, yes, but it's so worth it in the long run. You can be cautious of food (like dieting), but you should not be afraid of eating it. Food is a necessity and without it we cannot live, so don't EVER stop eating, or cut your food intake to a detrimental level.